Personally I think it's wise to keep the same avatar. While people may recognize your name when they read it, usually the first thing they see at a glance is the picture. And, if they've already associated your writing style with that picture, they will know to click without even reading the author's name. It's a form of branding that will help catch the attention of your fans quickly, in much the same way that many authors have their names written in the same font across multiple books. It's recognizable at a glance. If you do decide to change your avatar, however, I would recommend picking something that looks similar. For example, if it's a picture of you, just take a new picture in a similar location. Or, in my case, a new picture of a compass and a book.